76.13.44 problem 52

Internal problem ID [17626]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 52
Date solved : Tuesday, January 28, 2025 at 10:45:58 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 69

dsolve(a*x^2*diff(y(x),x$2)+b*x*diff(y(x),x)+c*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x^{\frac {a -b +\sqrt {a^{2}+\left (-2 b -4 c \right ) a +b^{2}}}{2 a}}+c_{2} x^{-\frac {-a +b +\sqrt {a^{2}+\left (-2 b -4 c \right ) a +b^{2}}}{2 a}} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 102

DSolve[a*x^2*D[y[x],{x,2}]+b*x*D[y[x],x]+c*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{-\frac {\sqrt {a} \sqrt {c} \sqrt {\frac {a^2-2 a (b+2 c)+b^2}{a c}}-a+b}{2 a}} \left (c_2 x^{\frac {\sqrt {c} \sqrt {\frac {a^2-2 a (b+2 c)+b^2}{a c}}}{\sqrt {a}}}+c_1\right ) \]